There has been proposed a light-emitting diode (LED) projector that uses a LED as a light-emitting element included in the light source device. The LED projector of this type includes a light source device having a LED, an illumination optical system into which light from the light source device enters, a light valve having a liquid crystal display plate into which light from the illumination optical system enters, and a projection optical system for projecting light from the light valve to a projection surface.
In the LED projector, to increase the luminance of a projected image, light loss must be prevented as much as possible on an optical path from the light source device to the light valve.
As described in Nonpatent Literature 1, there are restrictions based on etendue that are determined by the product of the area of the light source device and an emission angle. In other words, the light from the light source device is not used as projection light unless the value of the product of the light-emitting area of the light source device and the emission angle is set equal to or less than the value of the product of an incident surface area of the light valve and a capture angle (solid angle) determined by the F number of a projection lens.
Thus, in the light source device that includes the LED and an optical element into which light from the LED enters, reducing the light loss by lowering the etendue of light output from the optical element is an issue that requires attention.
In the light source device included in the LED projector, it is essential to achieve a projected luminous flux of about several thousand lumina by using a plurality of LEDs to compensate for a shortage of the amount of light emitted by a single LED.
As an example of such a light source using a plurality of LEDs, as shown in FIG. 1, Patent Literature 1 discloses a light source unit that includes a plurality of monochromatic light source devices 203a to 203f having LEDs 204a to 204f, optical axis matching members 202a to 202d for matching optical axes of lights output from monochromatic light sources 203a to 203f, light source sets 201a and 201b into which lights from optical axis matching members 202a to 202d enter, and light guiding device 200 into which the lights from light source sets 201a and 201b enter. In this light source unit, lights from the plurality of monochromatic light source devices 203a to 203f are synthesized, and lights that have emission angles narrowed by light source sets 201a and 201b enter light guiding device 200. In this configuration, light loss is reduced by narrowing the emission angles of the light incident on light guiding device 200 by light source sets 201a and 201b. 
As another example of the light source device using the plurality of LEDs, as shown in FIG. 2, Patent Literature 2 discloses a light source device that includes light source substrate 301 having a plurality of LEDs 300 arranged on a plane. This light source device includes an optical element having two prism sheets 304 and 305 each having prism columns formed on one surface and arranged by setting the prism columns to intersect each other, and frame body 303 for supporting prism sheets 304 and 305. In the light source device, lights from the plurality of LEDs 300 are synthesized by two prism sheets 304 and 305.